He's not saying they're equal, just that they're the same level of magnitude, for the purposes of a rough back-of-a-napkin approximation.

xkcd wrote:That’s enough to tell us that we’re talking about pile of moles on the scale of planets. It’s a pretty rough estimate, though, since it could be off by a factor of thousands in either direction.

I think Randall used the right formula for the volume of a sphere, but the formula he listed is for the SURFACE AREA (4 pi r^2); volume is (4/3) pi r^3.

Using the volume of earth (from wikipedia) as 1.08321 E12 km^3 (equivalent to radius = 6371 km), I calculate the extra radius of a sphere consisting of the volume of earth + the volume of moles to be 87 km, the amount by which the moles would cover earth.

By the way, I hope I'm not the only one for whom, in addition to the numbers "dozen" "billion" and "mole", this made think of "gross"

I think Randall has taken the wrong science to analyse the planet: it's not governed by biology but by chemistry:* The energy gained by removing the space between the moles and general compression is enough to bring the temperature in the core to 600K or more* There is also some radioactivity (Carbon 14, Cesium, Uranium, as found naturally inside earth animals) which - given some time and a proper fur isolation would bring the core temperature higher.* At these high temperature and given a reasonable time (10^6 years or more) we can assume that all carbon-carbon link will be broken at some point.

I believe that most metals would decant down to the core, a solid carbon cristal would form the outer core, and then there would be a huge water ocean, between 2 layers of ice.

solune wrote:I believe that most metals would decant down to the core, a solid carbon cristal would form the outer core, and then there would be a huge water ocean, between 2 layers of ice.

Note: I am assuming that the mole planet comes into being magically, *POOF*, like by a wish from a genie or by a powerful god (or God.) Not really any other possible way it could happen.

This might happen eventually, but it would take some time for the materials to separate and settle, and likely there would be large pockets of different elements throughout the crust or mantle of this mole planet (like in real planets.) Also, a question that comes to my mind is, how long would some, if any moles survive? Obviously the moles in the center (and at least 99%) of the planet would die very quickly due to intolerable pressures. And if there were no initial atmosphere, the ones one the outside would immediately freeze and die... but then the air expelled from their lungs would create a thin atmosphere, right? Since moles tunnel anyway, those ten to a hundred feet down might be okay for a while.

I can confirm that you can throw a mole, but they do not weigh anywhere near a pound... though Reggie does usually leave the entire mole on the porch for us (he's a sweet cat, from anyone else a dead rodent would seem creepy, but that's how cats say they love you enough to feed you... dead rodents) and I'd say a mole weighs about a third of a squirrel, and half a mole weighs about two thirds of a mouse... I'm pretty sure there is a little mountain of rodent bones in the field over the fence where I chuck them.

Incidentally: "That’s a neat coincidence I’ve never noticed before—a cubic mile happens to be almost exactly 4×π×r2 cubic kilometers, so a sphere with a radius of X kilometers has the same volume as a cube that’s X miles on each side.", is a great bit of random trivia.

mathmannix wrote: And if there were no initial atmosphere, the ones one the outside would immediately freeze and die... but then the air expelled from their lungs would create a thin atmosphere, right? Since moles tunnel anyway, those ten to a hundred feet down might be okay for a while.

if a while is not longer than a minute (basically how much time they can hold their breath, considering that they breathe 3 times faster than us) then I agree with you

mathmannix wrote:Note: I am assuming that the mole planet comes into being magically, *POOF*, like by a wish from a genie or by a powerful god (or God.)

I'm sure the Magratheans did it first. They don't judge their rich clients.

Second consecutive thread with references to the Guide. This is a winning week

If we had the tecnology (or magic) necessary to creat such Mole-Mole-Moon (can we call it MMM? ), I think we should wait and reserve it for when we really need it: deflecting an asteroid, or something.

One thing not covered in the article(?): what would happen on Earth, once we got our meaty new MMM? What impacts would it have in tides, sunlight, etc? Would it be better or worse for human kind than a ring of moles, as suggested above?

PolakoVoador wrote:One thing not covered in the article(?): what would happen on Earth, once we got our meaty new MMM? What impacts would it have in tides, sunlight, etc? Would it be better or worse for human kind than a ring of moles, as suggested above?

And most importantly - is the stench going to reach us? I'm pretty sure there will be occasional rain of decomposing moles when the mole-volcanoes (molecanoes?) erupt in the direction of earth, it shouldn't be hard to eject matter just strong enough so it overcomes the mole moon gravity and gets pulled towards earth. These will mostly burn on entry but everyone who has cooked expired meet knows that if you bake it start stinking even more - so the underlying question is, I guess, how much volcanic activity is there going to be?Another contributing factor will probably be solar winds that will blow particles from the mole moon our way once per rotation cycle - but what particles constitute the decomposing flesh smell? Are they subject to accelleration upon contact with solar wind?

I was also hoping we'll get a layer of oil around the core, where the pressure is enough to heat the delicious mole soup to sufficient temperature. If that's viable then I'm pretty sure oil companies are doing experiments on it - if they can pump oil from 10km deep or extract it from tar sands they can do anything.

The Moomin wrote:Would it be possible to breed enough moles to make rings around Earth, similar to those around Saturn, but out of moles?

Could we put the moles up a few at a time and add them in as time goes by until we have a mole of moles encircling the Earth, or would they have to be shot up as one?

Forming a ring seems more practical to me than making an entire planet of them.

Some quick wiki-fu leads me to believe that the ring vs moon argument would be settled by orbital position. There's a point called the Roche limit, it's the altitude below which an orbiting body would be pulled apart by the planet's gravity. Putting the moles in an orbit below the Roche limit would eventually turn them into a ring regardless of the creator's intent.

Unfortunately, my orbital mechanics are too weak to predict how stable the rings would be. There's some chance that the Moon we've already got would tend to pick up stray moles, sling them into space, or cause them to crash. That seems to be a solved problem in today's world of man-made satellites, but moles don't tend to have thrusters to help them keep orbit, so your mileage may vary.

On the other hand, trying to figure out where to put an entire second moon (and have it hold itself together) makes my brain hurt a little; the articles on co-orbital configurations start quoting math by Euler. My take-away was that it could be done, and that by picking an Earth-Moon Lagrangian point you could even build it up bit by bit as budget and mole population allows.

Max™ wrote:I can confirm that you can throw a mole, but they do not weigh anywhere near a pound... though Reggie does usually leave the entire mole on the porch for us (he's a sweet cat, from anyone else a dead rodent would seem creepy, but that's how cats say they love you enough to feed you... dead rodents) and I'd say a mole weighs about a third of a squirrel, and half a mole weighs about two thirds of a mouse... I'm pretty sure there is a little mountain of rodent bones in the field over the fence where I chuck them.

Incidentally: "That’s a neat coincidence I’ve never noticed before—a cubic mile happens to be almost exactly 4×π×r2 cubic kilometers, so a sphere with a radius of X kilometers has the same volume as a cube that’s X miles on each side.", is a great bit of random trivia.

Again, he's not saying that his math is right. Only that it's an approximation, for sort of order-of-magnitude calculations. Then he went back and did some research and all for the real numbers.

We used to do this sort of thing all the time with slide rules: the ruler gave you three-digit accuracy, more or less, but to figure out the order of magnitude took a separate calculation. And, in a pinch, you could simplify the numbers and get a pretty good answer even without a ruler.

Having become a Wizard on n.p. 2183, the Yellow Piggy retroactively appointed his honorable self a Temporal Wizardly Piggy on n.p.1488, not to be effective until n.p. 2183, thereby avoiding a partial temporal paradox. Since he couldn't afford two philosophical PhDs to rule on the title.

Vroomfundel wrote:And most importantly - is the stench going to reach us? I'm pretty sure there will be occasional rain of decomposing moles when the mole-volcanoes (molecanoes?) erupt in the direction of earth, it shouldn't be hard to eject matter just strong enough so it overcomes the mole moon gravity and gets pulled towards earth. These will mostly burn on entry but everyone who has cooked expired meet knows that if you bake it start stinking even more - so the underlying question is, I guess, how much volcanic activity is there going to be?Another contributing factor will probably be solar winds that will blow particles from the mole moon our way once per rotation cycle - but what particles constitute the decomposing flesh smell? Are they subject to accelleration upon contact with solar wind?

I'm pretty sure stench cannot travel vacuum, but stench-filled-flying-rotten-molecanoe'd moles totally can, and that is not going to be very nice

So I take it by these figures that there aren't enough of the requisite elements on Earth to construct even the smallest mole of moles, yes? Otherwise we'd already be under a sea of organic soup 80km deep, yes?

Is it plausible that there might be any exoplanets with the right balance of elements that something like that would be possible? A "meat planet", or otherwise a planet where a significant portion of its mass is chemically organic (and potentially alive)?

Pfhorrest wrote:So I take it by these figures that there aren't enough of the requisite elements on Earth to construct even the smallest mole of moles, yes? Otherwise we'd already be under a sea of organic soup 80km deep, yes?

Is it plausible that there might be any exoplanets with the right balance of elements that something like that would be possible? A "meat planet", or otherwise a planet where a significant portion of its mass is chemically organic (and potentially alive)?

Since there are something around a gazillion planets out there, my guess is: yes.

He's not saying they're equal, just that they're the same level of magnitude, for the purposes of a rough back-of-a-napkin approximation.

xkcd wrote:That’s enough to tell us that we’re talking about pile of moles on the scale of planets. It’s a pretty rough estimate, though, since it could be off by a factor of thousands in either direction.

And pi is about 5, for back-of-the-envelope purposes. (Not snarking, as I'm enjoying this new series.)

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.---If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

there are at least a few dozen mice, rats, voles, and other small mammals for every human.

I'm not interested.

Who wants mine?

mathmannix wrote:Note: I am assuming that the mole planet comes into being magically, *POOF*, like by a wish from a genie or by a powerful god (or God.) Not really any other possible way it could happen.

>Hi, I'm your genie. You have three wishes.<Cool. I want a million dollars.>*granted*<Wow. Can I have a mole of moles in space?>You bloody dumbass.. Granted, happy? Please be aware you have just one wish left to wish 'm away before they plummet to earth.<Can I have a Pepsi?

Max™ wrote:I can confirm that you can throw a mole, but they do not weigh anywhere near a pound... though Reggie does usually leave the entire mole on the porch for us (he's a sweet cat, from anyone else a dead rodent would seem creepy, but that's how cats say they love you enough to feed you... dead rodents) and I'd say a mole weighs about a third of a squirrel, and half a mole weighs about two thirds of a mouse... I'm pretty sure there is a little mountain of rodent bones in the field over the fence where I chuck them.

Incidentally: "That’s a neat coincidence I’ve never noticed before—a cubic mile happens to be almost exactly 4×π×r2 cubic kilometers, so a sphere with a radius of X kilometers has the same volume as a cube that’s X miles on each side.", is a great bit of random trivia.

Again, he's not saying that his math is right. Only that it's an approximation, for sort of order-of-magnitude calculations. Then he went back and did some research and all for the real numbers.

We used to do this sort of thing all the time with slide rules: the ruler gave you three-digit accuracy, more or less, but to figure out the order of magnitude took a separate calculation. And, in a pinch, you could simplify the numbers and get a pretty good answer even without a ruler.

Oh, I'm not nitpicking about the km/mile thing, it's an interesting coincidence.

ISS is shown in the earth-mole-crust scenario. Earth's gravity just increased by 0.76%, so at the same initial orbital velocity, the circular orbit becomes elliptical, with apogee radius staying the same, perigee radius dropping about 100 km, and the atmosphere rising about 80 km. This will increase the ram drag in front of the station by 75x at perigee, and 5x at apogee. The ISS orbit drops about 250 meters per day now, so the perigee will drop by about 1.3 km per day and the apogee about 19 km per day. The spiral decay will last less than a week before the final plunge into thick atmosphere. Perhaps some ISS astronauts will be in space suits, in one of the stouter modules, and survive until their fiery impact into the mole glop sea. If the mole sea is not already on fire, this should do it.

Since the station no doubt has its own internal DNS service, and relay systems such as the geosat band and TDRSS will stay aloft for centuries more, it is not quite fair to claim that the integrity of the DNS system is threatened - just diminished a whole bunch.

Or maybe not.

If the mole appearance is instantaneous, a few mole atomic nuclei will pop into existence close enough to atmosphere atomic nuclei to fuse. Most will come close enough to experience significant coulombic repulsion and release a lot of energy. The resulting planetary scale explosion will probably eject both mole and atmosphere into space at faster than orbital speeds, along with a lot of the crust, smashing ISS and everything else in orbit, and blasting the near side of the moon with incandescent mole gas. The mole goop will not turn into permanent rings - too hot, too volatile this close to the sun - but a few petatons of lunar and terrestrial rock will stay in orbit for a long time. A small fraction of the rock will encapsulate some bubbles of mole goop from the upper atmosphere, or globs of water from the ocean. Perhaps a few of those bubbles will support microbial life for a while, and later reseed the earth after the surface cools.

Will intelligent life re-emerge? Will they use DNS? They will be quite alien, but their crude stick figures may look like our stick figures.

brakos82 wrote:So now the Grand Question is.... what if Yoda pitched a mole of moles at 0.9c?

Well, the Lorentz factor for 0.9c is 1/sqrt(1-(0.9)^2) ~= 2.294, so the mass gained from acceleration is 1.294x the base mass. Multiply that by 4.92x10^22 kg, and multiply that by 9x10^16(i.e., c^2), and you wind up with a total energy imparted of 5.73x10^39 joules. For comparison, this is roughly 10^18 years of the current energy usage of human civilization, almost half a million years of the Sun's energy output, or some 10^28 Yoda-years.

(No, I don't have an easy way to roll the SAT question in - perhaps compare the energy used to pencil in the results of all the incorrect guesses?)

As a biologist, my first search after finishing the article was to look for bigger moles. "Really, Evolution? 75 grams? You can do better." As it turns out, the Russian desman (Desmana moschata) is the largest species of mole still alive. (I suspect that there were some larger moles, or talpids, as they are called [family Talpidae] around during the Paleogene, but I didn't find any documentation for this.*) D. moschata is positively huge compared to the Eastern mole, weighing in at about 520 grams. This may seem small and/or irrelevant, but this is an order of magnitude more massive (for values of 7 = 10). If my biologist brain is doing the right math right, we have 3.13x10^23 kg of talpids congregating in space now. That means 10 times the gravitational pull. But because the mole minor planet is twice as big in radius (assuming cube-root of 10 = 2), the surface gravity should be one quarter as strong. The two changes combine to effect a net increase of 2.5 times greater surface gravity. (Physicists, correct me if I'm wrong please.**) It's up to you if this makes a difference, but I think the 10-fold increase in mass would have interesting effects on the moles, the minor planet itself, and probably on Earth.

*

Spoiler:

Naturally, any scientific search about moles results in random hits throughout science where the text includes moles-the-unit. Makes me wonder how those who research moles search the literature, lol.

PolakoVoador wrote:One thing not covered in the article(?): what would happen on Earth, once we got our meaty new MMM? What impacts would it have in tides, sunlight, etc? Would it be better or worse for human kind than a ring of moles, as suggested above?

And most importantly - is the stench going to reach us?

That smell could be anything; a faulty stench coil, some cheese on the lens, who knows?